Kinks in composite scalar field theories

TL;DR

The work develops a systematic method to construct composite scalar field theories whose kink spectra can be identified analytically by coupling two parent models on a product target space via a parametric superpotential $W(\phi,\psi)$. It introduces a general extension with $W(\phi,\psi)=\alpha W_A(\phi)+\beta W_B(\psi)+\sigma W_A(\phi) W_B(\psi)$, derives the corresponding Bogomol'nyi equations and vacuum structure, and analyzes energy expressions and orbit flows to determine when kink families arise. Two explicit realizations are studied: (i) an extended planar double $\phi^4$ system exhibiting $\sigma$-driven transitions and rich kink sectors, and (ii) a three-field sine-Gordon generalization with a cube-vertex vacuum manifold, boundary/face/interior kinks, and explicit energy relations that grow with the coupling. The framework preserves analytical information from the original models while enabling controlled insertion of extra vacua and internal kink structure, with potential applications to condensed-matter and cosmological contexts and possible extension to Sigma-models.

Abstract

In this work, families of kinks are analytically identified in multifield theories with either polynomial or deformed sine-Gordon-type potentials. The underlying procedure not only allows us to obtain analytical solutions for these models, but also provides a framework for constructing more general families of field theories that inherit certain analytical information about their solutions. Specifically, this method combines two known field theories into a new composite field theory whose target space is the product of the original target spaces. By suitably coupling the fields through a superpotential defined on the product space, the dynamics in the subspaces become entangled while preserving original kinks as boundary kinks. Different composite field theories are studied, including extensions of well-known models to wider target spaces.

Figures (4)

• Figure 1: Vacua of the field theory (top panels) and its corresponding potential (bottom panels) for $\sigma=1$ (left), $\sigma=\frac{3}{2}$ (middle) and $\sigma=3$ (right). In the upper panels, the four fixed vacua are represented in black while the variable ones are depicted in red.
• Figure 2: Contourplot of the orbits of the emerging families of kinks (top panels) for different values of the constant $C$ for $\sigma=1$ (left panels), $\sigma=\frac{3}{2}$ (middle panels) and $\sigma=1000$ (right panels) and energies \ref{['eq:EnergiesFirst']} of the boundary and isolated kinks (bottom panels). The four fixed vacua are represented in black while the variable ones are depicted in red. Boundary and isolated kinks are represented in black.
• Figure 3: Vacua of the field theory (top panels) and the corresponding potential (bottom panels) for $\sigma=1$ (left), $\sigma=\frac{3}{2}$ (middle) and $\sigma=3$ (right). In the top panels, the four inherited vacua are shown in black while the extra ones are depicted in red.
• Figure 4: Contourplot of the orbits of the emerging family of kinks (top panels) for different values of the constant $C$ for $\sigma=1$ (left), $\sigma=\frac{3}{2}$ (middle) and $\sigma=3$ (right) and energies \ref{['eq:EnergiesPhi4Double']} of boundary and isolated kinks (bottom panels). The four inherited vacua are represented in black while the extra ones are depicted in red. Boundary and isolated kinks are represented in black.